Abstract

In this paper we propose a time-variant photonic crystal, which can be formed by a stream of wave-length-scale microdroplets flowing through a microfluidic channel. The functionality stems from the photonic bandgap generated from the 1D periodic perturbation of refractive index. The periodicity, volume fraction and composition of both the dispersed and the continuous phases can be conveniently tuned in real time by hydrodynamic or pneumatic methods. By simulation, it is found that the time-variant nature of the proposed structure can induce an abnormal energy evolution, which is distinct from any existing photonic crystal structures. As a basic component for optofluidic systems, the droplet-based photonic crystal may find potential applications in light modulation and light confinement, and could be an ideal model for pursuing physical insights into time-variant optofluidic systems.

Carbon disulifide (CS2) sometimes can be used as infrared transparent solvent, whose transparent window mainly spans at wavelengths from 8 to16µm. We select it because of its high refractive index which is 1.628. The most popular infrared solvent is carbon tetrachloride (CCl4), which is transparent at all wavelength less than 12µm. Other infrared transparent solvents include tetrachloroethylene, chloroform, dimethylformamide, dioxane, cyclohexane and benzene.

Carbon disulifide (CS2) sometimes can be used as infrared transparent solvent, whose transparent window mainly spans at wavelengths from 8 to16µm. We select it because of its high refractive index which is 1.628. The most popular infrared solvent is carbon tetrachloride (CCl4), which is transparent at all wavelength less than 12µm. Other infrared transparent solvents include tetrachloroethylene, chloroform, dimethylformamide, dioxane, cyclohexane and benzene.

The two-dimensional FDTD model and results of the TvPC structure. (a) The model of as-proposed droplet-based TvPC waveguide for calculation. (b) The empty waveguide model for reference. (c) The transmittance vs. frequency observed at the output point when the waveguide is excited at the light source point.

Energy evolution in droplet-based 1D TvPC. (a) The energy distributions in a finite TvPC at the 1st and the 2nd order waveguide modes, respectively. The waveguide is excited by a continuous source outside the left end of the channel. (b)-(e) The 1st and 2nd order energy distributions in an infinite 1D droplet-based TvPC at (b) t = 0, (c) t = T/4, (d) t = T/2 and (e) t = 3T/4, where T is the time period for the TvPC to restore. The dashed arrows indicate the evolution of electromagnetic energy, along with the flow of microbubbles.

Relationships between transmittance and lengths of microbubbles. (a) Schematic illustration of different microbubble sizes L. (b) The transmittance spectra of the 1D TvPC waveguide for different microbubble lengths, of 1.0a, 1.2a, 1.4a, 1.6a, respectively.

Relationships between transmittance and RI of continuous phase adopted in droplet-based 1D TvPCs (a) The transmittance of TvPC with different RIs, where center frequencies of the bandgaps are marked by orange triangles. (b) The center frequency of the bandgap as a function of RIs.

Light modulation at the bandedge frequency of the droplet-based 1D TvPC. (a) The energy evolution at the frequency f = 0.31c/a, in a time period T. (b) The transmission spectra of the waveguide at t = 0, t = T/4, t = T/2, t = 3T/4, respectively. (c) The transmittance modulation at f1 = c/a, f2 = 0.33c/a, respectively, as a function of time from 0 to 5T.

Relationships between defect lengths and defect mode frequencies. (a) Schematic models showing different defective TvPCs produced by inserting a longer liquid section at the center. The defect length d is defined to be the distance between two bubbles closest to the center. (b) The transmittance spectra of the defective TvPC, where the dashed arrows indicate the shifts of the defect mode by variation of d. (c) The plot of defect mode frequency as a function of defect length.

Behaviors of dynamic defects in droplet-based 1D TvPC. (a) Electromagnetic energy distribution in a defective TvPC waveguide at t = 2.5T, t = 3.5T, t = 4.5T, t = 5.5T and t = 6.5T, the defect length is 3.2a. The points with highest energy density are marked by orange triangles. (b) Transmittance spectra of the defective TvPC, where the defect mode peaks are clearly shown. (c) The transmittance at the defect mode frequency as a function of time, from 0 to 9T, the period for a dynamic defect to flow through the TvPC structure; blue circles are data points, and the red line is only guide for eyes.